Band structure of silicene on zirconium diboride (0001) thin-film surface: Convergence of experiment and calculations in the one-Si-atom Brillouin zone

Abstract

So far, it represents a challenging task to reproduce angle-resolved photoelectron (ARPES) spectra of epitaxial silicene by first-principles calculations. Here, we report on the resolution of the previously controversial issue related to the structural configuration of silicene on the ZrB2(0001) surface and its band structure. In particular, by representing the band structure in a large Brillouin zone associated with a single Si atom, it is found that the imaginary part of the one-particle Green's function follows the spectral weight observed in ARPES spectra. By additionally varying the inplane lattice constant, the results of density functional theory calculations and ARPES data obtained in a wide energy range converge into the "planar-like" phase and provide the orbital character of electronic states in the vicinity of the Fermi level. It is anticipated that the choice of a smaller commensurate unit cell for the representation of the electronic structure will be useful for the study of epitaxial two-dimensional materials on various substrates in general.

Progress in the materials science of silicene

“…Note that the importance of this phase lies in its relevance for epitaxial silicene: while for freestanding layers, the planar-like phase is less stable than the regularly buckled form of silicene [10], in its form with stripes [26], it becomes the ground state on the ZrB 2 surface [10, 27]. Note that it has also been calculated to form on the Ag(111) surface [28].…”

“…For instance, in our original [4] and subsequent studies [27, 52–54], structural evidence for epitaxial silicene on diboride thin films grown on Si wafers has been obtained from atomic-resolution surface imaging using STM, chemical information such as on the elemental composition and the chemical environment of Si atoms from high-resolution, core-level photoelectron spectra measured at a synchrotron radiation facility, and band structure-related information from the combination of angle-resolved photoelectron (ARPES) spectra and DFT calculations. Complementary and additional structural information might be obtained for instance by reflection high-energy electron diffraction (RHEED) [49], low-energy electron diffraction (LEED) [52] and from the analysis of incident electron beam energy dependent intensities ( I – V ) of LEED spots [55].…”

“…While initially [4, 53], our interpretation related to the buckling of epitaxial silicene on the ZrB 2 (0001) thin film surface leaned towards a metastable, so-called ‘regularly-buckled-like’ phase, the controversial issue in favor of the theoretically preferred ‘planar-like’ structural modification [10], shown in figures 5(d) and (e), in the top and side views, respectively, has been only resolved in very recent work [27] by finding substantial agreement between the results of DFT calculations and ARPES data obtained in a wide energy range. That is, it turns out that the substrate–silicene hybrid electronic band structure can be the most useful fingerprint of the structural configuration of adsorbed Si layers, a fact that is due to the high sensitivity of electronic to structural properties.…”

“…As our work shows, the agreement between calculations and the ARPES spectra has in part been achieved by slightly increasing the in-plane lattice constant. It has been pointed out that this has been necessary in order likely to account for a misestimate of the exchange-correlation energy in the generalized gradient approximation and to simulate the effect caused by the larger lattice constant of ZrB 2 thin films and the expected lower surface density of the Si atoms induced to avoid epitaxial strain [27]. …”

“…Figures 6(a) and (b) show the measured ARPES spectra along the –K Si direction of epitaxial silicene on ZrB 2 thin film as a function of the in-plane wave number k || [27]. Note that due to the (√3 × √3) reconstruction of the Si honeycomb layer, the K Si and M Si points of unreconstructed, hypothetical, freestanding silicene (with a unit cell containing two Si atoms) coincide with the and points of the repeated Brillouin zone of the reconstructed surface, respectively.…”